The realization space is
  [1   1   x1 - 1   0   0   1   x1    1   x1^2 - x1    1    1]
  [1   0       x1   1   0   1   x1    0        x1^2   x1   x1]
  [0   0        0   0   1   1    1   x1      x1 - 1   x1    1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^12 - 6*x1^11 + 14*x1^10 - 15*x1^9 + 3*x1^8 + 12*x1^7 - 16*x1^6 + 9*x1^5 - 2*x1^4)
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x1, x1 - 2, x1^2 - 3*x1 + 1, x1^2 - x1 - 1, x1^2 - x1 + 1, 2*x1 - 1, x1 + 1, 2, x1^2 + x1 - 1]